Even in advance of the 54-46 party-line Senate vote, the stock market dropped as fears spread that the first shutdown in 17 years would inconvenience millions and harm the economy. “We’re at the brink,” said Sen. Barbara Mikulski, D-Md., as House GOP leaders calculated their next move.

Ironically, the issue at the core of the dispute, implementation of key parts of “Obamacare,” will begin Tuesday on schedule, shutdown or no.

As lawmakers squabbled, President Barack Obama urged them instead to “act responsibly and do what’s right for the American people.”

At the White House, he said he was willing to discuss long-term budget issues with members of Congress, and expected to do soon. But, he added, “The only way to do that is for everybody to sit down in good faith without threatening to harm women and veterans and children with a government shutdown.”

Obama’s Democratic allies prevailed easily in the Senate on a vote to reject the latest House-passed bill, a measure that would delay the new health care law for a year and repeal a tax on medical devices that helps play for the program.

Anticipating their legislation would be rejected, House Republican leaders met in Speaker John Boehner’s office to plan their next move. Officials said that even though time was running short, they expected at least one more attempt to squeeze a concession from the White House, likely a demand to force a one-year delay in the requirement for individuals to purchase health coverage or face financial penalties.

A shutdown would cause an uneven impact across the face of government, inconveniencing millions.

About 800,000 federal workers, many already reeling from the effect of automatic budget cuts, would be ordered to report to work Tuesday for about four hours — but only to carry out shutdown-related chores such as changing office voicemail messages and completing time cards. Once they departed, they would be under orders not to do any government work.

Some critical services such as patrolling the borders, inspecting meat and controlling air traffic would continue. Social Security benefits would be sent, and the Medicare and Medicaid health care programs for the elderly and poor would continue to pay doctors and hospitals.

For the first time since the showdown began more than a week ago, there was public dissent from the Republican strategy that has been carried out at the insistence of tea party-aligned lawmakers working in tandem with GOP Sen. Ted Cruz of Texas.

Rep. Charles Dent, R-Pa., said he was willing to vote for stand-alone legislation that would keep the government running and contained no health care-related provisions. “I would be supportive of it, and I believe the votes are there in the House to pass it at that point,” he said.

Dent added he has been urging the Republican leadership to allow a vote along those lines.

A second Republican, Rep. Doug Lamborn of Colorado, said, “We haven’t given up on Obamacare ... but for this week we may have to give up. We tried everything and Harry Reid won’t budge,” he said of the Senate majority leader.

In response, a spokesman for Boehner said the leadership would discuss options with the rank and file at a closed-door meeting later in the day.

On Sunday, Sen. Susan Collins, R-Maine, said she, too, was ready to vote to keep the government open without conditions.

In remarks Monday on the House floor, Boehner criticized the Senate for taking the day off on Sunday, after the House had passed legislation shortly before 1 a.m. “Well my goodness, if there’s such an emergency, where are they?” he said.

Other Republicans sought to blame Democrats for any shutdown, but Dent conceded that Republicans would bear the blame, whether or not they deserved it.

The last time the government shutdown, in 1996, Republicans suffered significant political damage, and then-President Bill Clinton’s political fortunes were revived in the process.

Now, as then, Republicans control the House, and senior lawmakers insist even a shutdown isn’t likely to threaten their majority in the 2014 elections. “We may even gain seats,” Oregon Rep. Greg Walden, who chairs the party campaign committee, said recently.

For all the controversy about other matters, the legislation in question is a spending bill — and there was little if any disagreement about the spending-related issues.

The House and Senate have agreed to fix spending for a wide swath of federal programs at an annual level of $986 billion.

Without separate legislation to make further reductions, across-the-board cuts would automatically take effect early next year that would reduce the level to $967 billion.